### Abstract

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.

Original language | English (US) |
---|---|

Pages (from-to) | 931-938 |

Number of pages | 8 |

Journal | Physical Review E |

Volume | 48 |

Issue number | 2 |

DOIs | |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E*,

*48*(2), 931-938. https://doi.org/10.1103/PhysRevE.48.931

**Escape problem for irreversible systems.** / Maier, Robert S.; Stein, D. L.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 48, no. 2, pp. 931-938. https://doi.org/10.1103/PhysRevE.48.931

}

TY - JOUR

T1 - Escape problem for irreversible systems

AU - Maier, Robert S.

AU - Stein, D. L.

PY - 1993

Y1 - 1993

N2 - The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.

AB - The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotic behavior of fundamental quantities such as the mean escape time. In this paper we present a general technique for analyzing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the asymptotic behavior of the mean escape time depends on the dynamics of the system along the most probable escape path. We also present results on short-time behavior and discuss the possibility of focusing along the escape path.

UR - http://www.scopus.com/inward/record.url?scp=18144390105&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144390105&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.48.931

DO - 10.1103/PhysRevE.48.931

M3 - Article

AN - SCOPUS:18144390105

VL - 48

SP - 931

EP - 938

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -